If it was right under the circle platforms, then it would probably be in
the same place as the victoria line running tunnels just before the
platforms.
The Victoria platforms are two level above the Northern ones; do the
tunnels dive so quickly to the west that there isn't room for a set of
platforms next to the Northern line? I'd be surprised if that was true.
And how would you get an escalator anywhere without it hitting the
victoria line running tunnels (if heading east or west) or the
northern line platforms (if heading north)?

It would only work if it was much deeper than the northern line (so
that escalators could head north without running into the northern
line), or to the north (so that they could head east/west).

KX Thameslink is far to the south east of the other platforms;
Well, east, anyway. The station building is 150-odd metres east of the
junction of York Road and Euston Road; that junction is very roughly the
eastern end of the Northern line platforms, and the western end of the
Victoria platforms.
Its further than the end of the victoria line - the connecting tunnels
are very long, and only just reach the far end of the KX thameslink
platforms.

If the Chelsea-Hackney platforms were to the east, like the Victoria
platforms, a link to the old Thameslink station at their eastern end would
be quite plausible. You'd have a link to the 1960s ticket hall,
How? There isn't any room to fit another connection in. It can't head
through the south wall of the ticket hall because it would bisect the
fleet river and the circle line running tunnels, and if it heads
through the north wall its going in completely the wrong direction -
it would basically meet up with the northern ticket hall tunnels.

perhaps the Circle platforms, at the western end.
The problem with that is that the only way it can go is south or north
from those platforms, because directly underneath them, and to the
east and west of underneath as well, is the victoria line running
tunnel. I've always wondered why they never built the victoria line
platforms there instead - it would have allowed better connections to
the other lines - perhaps there's an additional obstruction around
there as well.

You might also manage a
link to the Victoria or Piccadilly platforms at that end
- indeed, the only way to get to the ticket hall might be a link up to the Victoria
concourse,
The problem with that is there is already an obstruction at the west
end of the Victoria line concourse - the escalators. You can't remove
them to put in a connection to the chelsea-hackney; it would be self-
defeating. And if you put it much further along the concourse you
basically have it facing the wrong direction - it forces people to use
the victoria line platforms themselves just to reach the ticket hall,
which is a recipe for congestion nightmares.
The Piccadilly platforms are even worse - they have escalators to the
ticket hall AND the northern line at that end - the congestion there
is already atrocious, so even if you managed to find a gnats breadth
in which to place the escalators to the chelsea-hackney you'd jam the
entire station due to the congestion.

You might even manage a link from the Victoria to the Thameslink station.
Isn't there something like this at the moment?
There's a long awkward link to the Thameslink station. But sometimes
its quicker to walk on the surface.

The major advances in civilization are processes that all but wreck the
societies in which they occur. -- Alfred North Whitehead
Like Solon?